It's never made a difference to me in years of doing chromakeys.
It's not the shirt, unless it has some green in it. It's more about the even lighting of the background with good saturation and the contrast ratio. I suspect the latter is your big problem on this one. Not that you need to blow out the shot with the green amped up at like 98 IRE. But you need a clear difference in that brightness to make the key work. Just to pull a number out of my ear, say, 20-30 IRE units difference makes me happy.
Your other problem may be spill contaminating the edge of the key. A black shirt, if shiny, could easily pick up green spill if you don't have a good distance from the screen. If the space you're in doesn't allow that distance, you can backlight the talent using magenta gels to counter the green. On a blue screen stage, you'd use a bastard amber or straw colored gel. These can be faked in post somewhat, I know that in Apple's chromakeyer they have edge enhancement tools that will apply and adjustable amount of spill-killing color to edges. You can overdo this easily, be careful.